Answer:
0.76 s
Explanation:
We use the formula for rotational speed, ω given its rotational acceleration α . ω = ω₀ + α(t - t₀) where ω₀ = initial rotational speed, ω = final rotational speed, ω₀ = initial rotational speed, α = rotational acceleration and t = initial time and t₀ = final time.
Since the wheel starts from rest, ω₀ = 0 and t₀ = 0. Given that α = 220 rad/s² and ω = 1600 rpm = 1600 × 2π/60 rad/s = 167.55 rad/s. Substituting these values into the equation ω = ω₀ + α(t - t₀)
167.55 = 0 + 220(t - 0) = 220t
So, t = 167.55/220 = 0.762 s ≅ 0.76 s
So, it takes the wheel 0.76 s to attain this rotational speed